MTH 102 UNLV Compute the Values Using Exponential Functions Algebra Questions

Math 1025.1 Exponential Functions
I.
II.
III.
IV.
Graph of Exponential Functions
Transformations of Graphs of Exponential Functions
Exponential Growth Models
Exponential Decay Models
V.
The Number​
e
●
Definition: If b is a positive number,
●
Form of exponential functions:
●
Examples of exponential functions
Example 1: Graph
y = a (bx − h ) + k
vs.
Non-examples of exponential functions
y = 2x
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Notice that
●
Definition:
Graphs of Exponential Functions:
●
Equation:
●
x − intercept :
●
y − intercept :
●
Domain:
●
Range
●
Horizontal Asymptote:
x
When b > 1 for y = b
x
When 0 < b < 1 for y = b ​or when −x b > 1 for y = b
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Transformation of Graphs of Exponential Functions
Example 2:
a.
b.
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c.
Exponential Growth Models:
Exponential Growth Models look like
●
Equation:
●
x − intercept :
●
y − intercept :
●
Domain:
●
Range
●
Horizontal Asymptote:
●
Shape:
The exponential growth function:
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Example 4:
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x
Example 5: An antique table increases in value according to the function v (x) = 900(1.05) dollars, where x is
the number of years after 2000.
(a) How much was the table worth in 2000?
(b) If the pattern indicated by the function remains valid, what is the value of the table in 2004?
(c) Use a table to estimate the year when this table would reach double its 2000 value.
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Exponential Decay Models:
Exponential Growth Models look like
●
Equation:
●
x − intercept :
●
y − intercept :
●
Domain:
●
Range
●
Horizontal Asymptote:
●
Shape:
Examples of Exponential Growth
vs.
Examples of Exponential Decay
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The Number​
e
e≈
The exponential function with base
e occurs frequently in _____________ and in ______________.
The growth in value compounded continuously of investment is another important application that can be
modeled by an exponential function. The function of investment compounded continuously is given by
Example 5:
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